Problem: $f(x) = \sqrt{ x - 8 }$ What is the domain of the real-valued function $f(x)$ ?
Solution: $f(x)$ is undefined when the radicand (the expression under the radical) is less than zero. So the radicand, $x - 8$ , must be greater than or equal to zero. So $x - 8 \geq 0$ ; this means $x \geq 8$ Expressing this mathematically, the domain is $\{ \, x \in \RR \mid x \geq8\, \}$.